Interval (or Bounded-Parameter) Markov Decision Processes (IMDPs) are a class of uncertain finite-state Markov Decision Processes (MDPs), where transition probabilities between states are only known to belong to intervals [1]}. Due to their modelling flexibility and the availability of efficient planning algorithms [1]}, IMDPs have recently gained popularity in the control and computer-science communities for verification of and control-synthesis for uncertain systems (see, e.g., [3]}, [4]}, [5]}, [6]}, [7]}). However, due to the absence of computational algorithms for IMDPs with continuous-action spaces, the action set is, generally, assumed discrete [3]}, [4]}. This is a restrictive assumption as many realistic control applications involve continuous underlying action spaces. Furthermore, with the current available algorithms, the only way to address continuous action-spaces is either a) to discretize the action-space and deal with discrete-action IMDPs, or b) solve the optimization problems associated to control synthesis using heuristics, as recently proposed in [5]}. Nonetheless, a) scales exponentially with the dimension of the action space, rendering high-dimensional problems intractable. Finally, b) - and a), when the discretization is carried out blindly - results into suboptimal solutions without suboptimality bounds.
